Phase mixing of relativistically intense longitudinal wave packets in a cold plasma

Abstract

Phase mixing of relativistically intense longitudinal wave packets in a cold homogeneous unmagnetized plasma has been studied analytically and numerically using the Dawson Sheet Model. A general expression for phase mixing time (ωptmix) as a function of amplitude of the wave packet (δ) and width of the spectrum (Δk/k) has been derived. It is found that the phase mixing time crucially depends on the relative magnitude of amplitude “δ” and the spectral width “Δk/k”. For Δk/k≤2ωp2δ2/c2k2, ωptmix scales with δ as ∼1/δ5, whereas for Δk/k>2ωp2δ2/c2k2, ωptmix scales with δ as ∼1/δ3, where ωp is the non-relativistic plasma frequency and c is the speed of light in vacuum. We have also verified the above theoretical scalings using numerical simulations based on the Dawson Sheet Model.